Functional integral method for investigating the dynamics of a Dicke type model

An approach is proposed to the investigation of the dynamics of model systems based on representation of the density matrix and generating functional of the temperature-time Green's functions in functional integral form. The equations for the Green's functions obtained in this scheme are investigated, together with methods of their approximate solution. For a Dicke type model the possible dynamical regimes describing processes of nonlinear optics are determined. The dependence of the condition of onset of a phase transition in the system on the statistics of the fields of the medium is established.